As you describe, people may buy self driving cars and use the self-driving feature to drive them more often. Wealthy folks and people in rural areas are almost certain to take this route.
Others predict that people won't buy cars at all and will instead rent them from ride services, who in turn may promote ride sharing on an unprecedented scale. Poor folks, for whom a car is a major expense, are almost certain to take this route, as well as city dwellers.
Personally, I think we may see traffic increase in some areas and substantially decrease in others. I suspect the largest source of traffic -- the commute -- will shrink considerably as networks of reasonably dense self-driving vanpools and small busses pop up.
>> reasonably dense self-driving vanpools and small busses pop up.
Utopia much?
However, it's not like paying a driver $100/day to drive a minibus around to pick people up and drop them off is likely the reason that isn't a widespread service today. So someone would need to explain to me why self-driving changes that equation.
Quite rational reasons for why a driverless taxi won't work.
sandworm101 mentioned "People own cars for irrational reasons". I wanted to add some rational reasons for owning a car, beyond what RightMillennial wrote.
Many people don't have a car and don't need a car. The point is that there are reasons for owning a car beyond 'irrational' things like fashion and coolness.
That said, I agree that habits can change. Car-pooling was probably more common at one point than it is now. On the other hand, a lot of people seem to favor Uber because they don't want to deal with public transit even when it's available.
I think people avoid public transit because it is necessarily slow due to the multiple stops. They may also avoid it because it is too accessible. Sharing a vehicle with other commuting professionals is a vastly different experience than what you'll find on most public transit.
Consolidate taxi/minibus/event bus/medical&elderly ride/mass transit into a pool of vehicles available 24/7 with resources for surge times/maintenance/cleaning etc, and this will become the norm easily enough.
Then it's just a question of who operates and at what cost?
[1] https://www.theverge.com/2018/3/12/17109708/via-arlington-te...
Dynamic routes based on individual demand, grouping together a small number of people into a quick access people carrier. E.g I want to go right across town, you have a shorter journey that roughly overlaps my route, the vehicle will deviate slightly to pick you up.
The second thing to consider is the opportunity for mass-transit level control of autotaxi fleets (or all cars in a glorious future where everything is awesome(tm)). Optimsing the merging and cross traffic flows beyond what traffic lights do today.